Selecting all coplanar vertices from another mesh
Select all co-planar verts in other edit meshes based on 3 selected verts of active mesh.


3 selected verts form a plane. The coordinate of one and the cross product of vectors formed by two &quot;edges&quot; is the normal.

For all other meshes select their verts based on there distance from plane defined in step above.

mathutils.geometry.distance_point_to_plane is a utility function that returns the distance of a point to a plane.

The vert coordinates of other meshes are converted to the local space of active object to perform the test. Could instead use global coordinates. To make a local normal global see Python: vertex normal according to World


Test script. Select objects of interest and enter edit mode (2.8+). Select 3 verts of same object and run script. Any verts in the same plane (within tolerance) are selected in other meshes.
import bpy
import bmesh

from mathutils.geometry import distance_point_to_plane as dp2p

TOL = 1e-4

context = bpy.context

ob = context.edit_object
mw = ob.matrix_world
mwi = mw.inverted()
obs = [o for o in context.selected_objects if o.type == 'MESH']
obs.remove(ob)

bm = bmesh.from_edit_mesh(ob.data)

# using face normal
'''
f = bm.faces.active
plane_no = f.normal
plane_co = f.calc_center_median()
'''
# using 3 verts from select history
v1, v2, v3 = bm.select_history[-3:]
plane_co = v1.co
plane_no = (v1.co - v2.co).cross(v3.co - v2.co).normalized()
# should assert all verts and not inline.
for o in obs:
    bm = bmesh.from_edit_mesh(o.data)
    M = mwi @ o.matrix_world
    for v in bm.verts:
        v.select_set(
                abs(dp2p(M @ v.co, plane_co, plane_no)) &lt;= TOL              )
    bmesh.update_edit_mesh(o.data)